Abstract:
A Chaitin Omega number is the halting probability of a universal Chaitin (selfdelimiting
Turing) machine. Every Omega number is both computably enumerable
(the limit of a computable, increasing, converging sequence of rationals) and random
(its binary expansion is an algorithmic random sequence). In particular, every
Omega number is strongly non-computable. The aim of this paper is to describe a
procedure, which combines Java programming and mathematical proofs, for computing
the exact values of the first 63 bits of a Chaitin Omega:
000000100000010000100000100001110111001100100111100010010011100.
Full description of programs and proofs will be given elsewhere.
